Organiser: Liam Naughton (NUI Galway)
A postgraduate conference will be held on Monday April 6th. The morning schedule will consist of a series of talks. This is an opportunity for mathematics students to present their research to an audience of peers. Attendance by anyone other than postgraduate students is strictly by invitation only.
Posters will be exhibited on the university concourse throughout the conference.
Once you have registered for the BMC/IMS on the main registration page please direct all enquiries to
All talks will be held in the McMunn Theatre on the university concourse.
9:30-9:50 Ben Fairbairn
Title : You take the high road and I'll take the low road : Extending Symmetric Generating Sets.
This is joint work with RT Curtis. Exhibiting generating sets
for groups that have an underlying highly symmetric combinatorial
structure has proved extremely useful in providing new existence proofs
for various groups (most notably the sporadic simple groups) and for
providing a succinct means of representing their elements. Since it is
naturally much easier to find symmetric generating sets for smaller groups
than larger groups it is natural to seek means of extending symmetric
generating sets to larger symmetric generating sets. In this talk we
describe some previously used approaches to this problem to highlight
their weeknesses before describing a new more flexable approach to this
problem and giving an explicit example relating to the groups SU_3(2^r).
10:00-10:20 Nicholas Korpelainen
Title : How to tell a friend from a foe : What every algorithmic graph problem should know about graph classes.
Why are some graphs easier to deal with than others for difficult
algorithmic problems? Indeed, many NP-complete graph problems (such as
finding a maximum independent vertex set) can be made polynomial-time
solvable by restricting to an interesting subclass of all graphs. We will
discuss strategies for determining whether a graph class is 'friendly' in
this respect. We will also describe how to find minimal 'unfriendly' classes
of graphs. The talk will concentrate on examples and graph-theoretical
proofs, and it will be extremely light on the technical details of
10:30-10:50 Ana Lucia Garcia Pulido
Title : A geometrical approach to Morse Theory.
Morse Theory is a beautiful and helpful tool in Topology. In this talk, I
will explain some theorems of Morse Theory that help us understand the
topology of a compact manifold. I will try to give insight into the
geometrical decomposition in cells of a compact manifold via Morse Theory.
This talk will include examples to show how powerful Morse Theory can be.
11:00-11:30 Coffee Break
11:30-11:50 Anastasia Kisil
Title : Investigating the SL(2,R) invariant geodesic curves with the associated invariant distance function in parabolic geometry.
We investigate the SL(2,R) invariant geodesic curves with the
invariant distance function in parabolic geometry. Parabolic geometry
naturally occurs as action of SL(2,R) on dual numbers and is placed in
between the elliptic and the hyperbolic geometries (which arise from
action of SL(2,R) on complex and double numbers). Initially we attempt
use standard methods of finding geodesics but they lead to degeneracy
this set-up. Instead, by studying closely the two related hypercomplex
numbers we discover a unified approach to a more exotic and less
dual number's case. With aid of common invariants we describe the
distance functions that turn out to have some unexpected, interesting
12:00-12:20 David Barrett
Title : Statistics of Brain activity: Relating correlations to network connectivity.
Neurons in the brain, especially nearby neurons, are often correlated, in
the sense that activity in one set of neurons partially predicts the
activity in another. Determining the correlation structure in large neural
networks is critical for understanding everything from information storage
to network dynamics to computing to learning in the brain. Historically, the
main approach has been experimental, but the amount of data required to
accurately assess correlations scales very badly with the number of neurons.
We derive an expression which relates correlations to the network
connectivity and single neuron properties.
12:30-12:50 Marcus Bishop
A Quiver Presentation for the Descent Algebra of a Coxeter Group
Following a recent article of Goetz Pfeiffer that
describes a mechanism for producing a quiver presentation of the descent
algebra of a finite Coxeter group, we apply the method in the
case of the Coxeter group of type A by representing the elements of Pfeiffer's
presentation as sequences of binary trees. We intend to use the same method
to calculate quiver presentations for the other infinite families of